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Cancun, Mexico (CNN) -- Tropical Storm Rina continued to weaken Thursday as it began affecting some of Mexico's most popular beaches.
Forecasters warned that the storm could still bring heavy rains and destructive waves. Rina was packing sustained 60 mph (95 kph) winds -- a full 10 mph less than what it was hours earlier -- early Thursday evening, according to the U.S. National Hurricane Center.
As of 8 p.m. ET, tropical storm conditions were already evident on the Yucatan Peninsula, with the brunt of the stormy weather continuing to move northward overnight.
Rina will likely drop 3 to 6 inches of rain over the eastern part of the peninsula and Cozumel through Friday, with isolated amounts of up to 10 inches, according to the Miami-based weather agency.
A storm surge of as much as 1 to 2 feet above normal tide levels along the coast is expected, "accompanied by large and dangerous waves," the hurricane center said.
Authorities took numerous precautionary measures ahead of the storm, while numerous businesses in Cancun and elsewhere shut down in anticipation.
"First we're thinking, we're stranded in Cancun, there could be worse things," Amelie Jarvis, a tourist from Canada, told CNN. "But then we noticed that everything is closed. I don't know what we're going to do."
Thousands of people have been evacuated from islands and coastal areas, boating has been banned and several shelters have opened, some area area schools.
The evacuees include about 50,000 residents Quintana Roo state, which includes the resort towns of Cancun and Cozumel, because their housing was considered "vulnerable," said Juan Gabriel Granados, operations director for Quintana Roo civil protection in Chetumal. Most of them have moved inland to stay with relatives or friends, he added.
"We're asking both (residents) and tourists to remain calm. The state and local governments are ready for the hurricane," said Granados.
Alcohol sales were banned as of 7 p.m. Wednesday; transportation to Cozumel had been banned since 5 p.m., he added.
Beach-front businesses in Playa del Carmen boarded up ahead of the storm, as surfers took advantage of the choppy seas, Guillermo Camarena told CNN's iReport.
Residents of the area were relieved that the storm had weakened, but still worried about damage, since Hurricane Wilma devastated the area in 2005, Camarena said.
Tropical storm winds of 39 mph or stronger extended out 70 miles from the storm's center, which was about 35 miles south-southwest of Cozumel as of 8 p.m. Rina was then moving north at 7 mph.
Tropical storm warnings were then in effect in for the Yucatan Peninsula, from Punto Gruesa and Progreso.
The storm will not make landfall on U.S. soil, predicted Dennis Feltgen, a spokesman for the National Hurricane Center.
CNN's Ed Payne, Tom Watkins, Catherine E. Shoichet, Dana Ford and journalist Brisa Munoz of CNNMexico.com contributed to this report.